2b. Calculating 's at time t = 1

In the special case where t = 1, there are no paths to the
state. The probability of being in a state at t = 1 is therefore
the initial probability, i.e. Pr( state | t = 1) = (state), and we
therefore calculate partial probabilities at t = 1 as this
probability multiplied by the associated observation
probability;

Thus the probability of being in state j at intialisation is
dependent on that state's probability together with the
probability of observing what we see at that time.